looks to me like your disk file system is corrupt - at this point back up all the data you can on the drive, then format it and copy the data back (if the format succeeds without problems).
Then it looks somewhat more like the remnants of Windows updates.
Sudden random inaccessible directories could be file system corruption. Since it has been working for a long time since they appeared, probably not.
Right-click the folder, select properties. Choose the Security tab. Click Advanced. Choose the option to Take Ownership. Tick to Change Subfolders and Files. Apply, then try deleting the folder.
Ran out of Edit time, so more accurate instructions follow
This is for Windows 7, Windows Vista/XP will be broadly similar. If you don’t have a Security tab in Properties, you probably have Home edition - try doing this in Safe mode.